Which is Bigger?

Which is bigger 5/6 or 7/8? If the answer isn’t popping into your head in seconds, you are not alone. Fractions are one of the most misunderstood concepts among both young and old in mathematics. They don’t seem to follow the same rules as whole numbers. Many of us purposely never work with fractions at all, preferring to change them into decimals so we don’t have to deal with fractions.

Recently some co-workers and I posed this question to different groups of adults and it caused much controversy. No one was sure what to answer initially and there was some embarrassment about not knowing an answer. Many people were convinced initially that 5/6 was bigger because the “pieces that are sixths are larger than the pieces that are eighths.” After much discussion, several algorithms and drawings, and one number line, the groups finally decided that 7/8 is actually bigger.

This is no insult to these groups of colleagues. For a very long time our understanding of fractions has relied on memorizing procedures, rather than a deep conceptual understanding of fractions. We get mixed up between numerators, denominators, GCF, and LCM.

We want our students today to understand that fractions have a place on a number line just like a whole number. Students in 3rd through 5th grade are having experiences that are allowing them to construct an understanding of fractions, where they can decompose and compose fractions and understand why finding a common denominator to add fractions actually makes sense. Factors, multiples, and simplest form aren’t just terms to memorize for a single test. Instead, we want to start to see the connections between all these terms and connect them to previous understanding. Connections in mathematics are so important, and for the longest time we ignored them in favor of being able to calculate.

This consternation over the teaching of concepts that involve fractions was the impetus for the launch of the Research Division within the AIMS Center. We know that students often miss the critical components in their understanding that allow them to construct meaning around fractions. Perhaps in ten years, when a random group of adults are asked this same question of which is larger, there won’t be so much hesitation – thanks to teachers changing the culture of teaching and allowing students the chance to construct their learning within mathematics and other subjects.